Exhibit 32.1

CERTIFICATION OF CHIEF EXECUTIVE OFFICER AND

CHIEF FINANCIAL OFFICER PURSUANT TO

18 U.S.C. SECTION 1350, AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

Each of Andrew D. Ory and Peter J. Minihane hereby certifies, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, in his capacity as President and Chief Executive Officer (principal executive officer) and Chief Financial Officer and Treasurer (principal financial officer), respectively of Acme Packet, Inc. (the “Company”), that, to his knowledge, the Quarterly Report of the Company on Form 10-Q for the period ended March 31, 2012 as filed with the Securities and Exchange Commission (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 and that the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

This written statement is being furnished to the Securities and Exchange Commission as an exhibit to the Report, and “accompanies” such Report to which it relates, is not deemed filed with the Securities and Exchange Commission and is not to be incorporated by reference into any filing of the Company under the Securities Act of 1933, as amended, or the Securities Exchange Act of 1934, as amended (whether made before or after the date of the Report to which it relates), notwithstanding any general incorporation language contained in such filing. A signed original of this statement has been provided to the Company and will be retained by the Company and furnished to the Securities and Exchange Commission or its staff upon request.